On a certain island each of the inhabitants is a member of one of the two existing clubs.

The membership distribution is such that when two random people meet, the probability of those two belonging to the same club is equal to the probability of them belonging to distinct clubs.

When 100 newcomers arrive on the island and each enrolls in one of the two clubs, the distribution still retains this feature. How many people belong to either club?

The possibility that everyone belongs to both clubs seems to work. Is this permitted? This doesn't seem consistent, however, with difficulty rating = 4.

Posted by Richard on 2004-06-17 13:54:38